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Here we consider a model of an isolated vortex to understand the vertical dynamics induced by mesoscale eddies in the ocean. We use the analytical solutions to a balanced model for an ellipsoid of uniform potential vorticity to examine how the vertical motions induced depend on the vortex shape and its orientation, i.e. whether the vortex is vertically upright or tilted with respect to the vertical axis. The motion induced by the vortex can be divided into two kinds: (1) the interior flow which acts on the vortex itself and (2) the exterior flow which acts on its surroundings. For an upright ellipsoid, there are no self-induced vertical motions and the vortex rotates steadily about the vertical axis. However, for a tilted ellipsoid we find solutions exist where the vortex rotates about the vertical axis, while the vertical motions cause the tilt angle of the vortex to oscillate. This effect is stronger as the tilt angle is increased. Considering the exterior flow, there exists an exterior vertical velocity for the upright and tilted ellipsoids. However, the dynamics induced by the exterior vertical velocity is very different for the upright and tilted cases. We find that for an upright ellipsoidal vortex, the vertical motions are largest for vortices with high horizontal eccentricity and a vertical height-to-width aspect ratio near unity, vanishing as the horizontal cross-section of the vortex becomes circular. Instead for the tilted case, the vertical motions are largest when the horizontal cross section is circular, and for strongly prolate vortices, with the largest vertical motions occurring when the tilt angle is 45 ∘ . [ABSTRACT FROM AUTHOR]

A new mathematical analysis for the dynamics of laminar spray diffusion flames in the vicinity of a vortex flow field is presented. The governing equations for a spray evaporating in an unsteady vortex are studied. New similarity solutions are found for the dynamics of the spray and the flame it supports. Analytical solutions for the spray flames are derived using Shvab-Zeldovich parameters, through which the radial evolution of the flames is found. The results based on the solution reveal the significant effects vorticity and droplet evaporation have on the flame dynamics. An extinction analysis is carried out which maps the influence of the evaporation coefficient and vortex intensity on flame extinguishment. A number of competing factors such as vortex intensity and heat loss due to evaporation were found to be responsible for flame extinction. Despite the model’s simplicity, its predictions offer new insights into the driving mechanisms of more complex spray-combustion situations in which droplets are evaporating in vortical environments. [ABSTRACT FROM AUTHOR]

Wall deposition is one of the most conventional problems in the spray drying process. The operation of a spray dryer is affected by the wall deposition fluxes inside the equipment. In this study, computational fluid dynamic (CFD) simulation was used to investigate the effect of spray dryer geometry on wall deposition. A CFD model was developed for different geometries of spray dryer with a conical (case A) or a parabolic (cases B and C) bottom. The results implied that the parabolic geometry resulted in a lower deposition rate on the spray dryer walls. A comparison of results using the P-values (F-test) of the air velocity, in the conical and parabolic geometries, showed that there was a significant difference in air stability between them. The flow field in conical geometry case A was significantly more unstable, and parabolic geometry case C produced the most uniform airflow patterns. Moreover, the higher wall shear stress in case C, with lower values of the vorticity, would result in less wall deposition. [ABSTRACT FROM PUBLISHER]

We study statistics and structures of pressure and density in the presence of large-scale shock waves in a forced compressible isotropic turbulence using high-resolution numerical simulation. The spectra for pressure and density exhibit a −2 scaling over an operational definition of the inertial range. Both the numerical simulation and a heuristic PDF model reveal that the PDFs of pressure increment exhibit a −2 power law region for the separation in the operational definition of inertial range, quantitatively similar to the PDF of pressure gradient, which also displays a −2 power law region. Moreover, the statistical relation between density increment and pressure increment has been investigated through a shock-relation model. There is a positive correlation between the vorticity magnitude and pressure, which is different from the case of incompressible turbulence. We argue that this difference is due to large-scale shock waves, another type of intermittent structures in addition to vortex structures in incompressible turbulence. [ABSTRACT FROM AUTHOR]

The concept of conservation of power during scour by the primary vortex formed in front of caisson piers is used to develop a relation for the temporal of scour depth variation. To test this relation, experiments were conducted using two sediment beds, three types of caisson piers and four relative flow depths. The agreement between the temporal variation of scour depths from the present approach and the literature data is good. The computed values of other researchers also agree fairly with the present proportionality constants. An expression for scour duration to reach the equilibrium scour depth is deduced from the power concept based on long duration literature data. The validity of this expression is verified for the equilibrium duration concept. [ABSTRACT FROM PUBLISHER]

Through our extensive theoretical and numerical study, we present two theorems on vortex tubes and one corollary on ‘vortex breakdown’. First, we addressed that vortex cannot have ends inside the flow field and the only vortex tube that exists inside the flow field is the ring-like vortex with or without legs on the wall. In addition, we found that the widely spread statement vortex breakdown is theoretically impossible and can never happen inside the flow field. Flow transition in a boundary layer is not caused by vortex breakdown, but rather high shear layers near the wall. [ABSTRACT FROM AUTHOR]

We formulate a dynamically consistent two-layer quasigeostrophic model of geophysical flow using the concept of background currents which are characterized by a constant potential vorticity minimizing the energy. An incident current over a delta-like isolated topographic feature generates a topographically trapped vortex in the bottom layer with a singular elliptic point, and one with a regular elliptic point in the upper layer. Such vortices are finite regions of recirculation which occur in the vicinity of isolated topographic features. The corresponding Hamiltonian equations of motion for a fluid particle are known to produce chaotic advection under the presence of the periodic incident current. When a periodic incident current is superimposed, fluid is entrained and detrained from the neighbourhood of the vortex and chaotic particle motion occurs. At a small amplitude periodic incident current we have a near-integrable case of weak chaotization in narrow stochastic layer near separatrix. At a finite amplitude periodic incident current we have the case of strong chaos, which will be investigated here. For the bottom layer of the flow, there is always a regular region (regular vortex core) around the singular elliptical point even in the case of a finite amplitude periodic incident current. Particles in this regular region have regular trajectories and will remain there permanently, whereas particles with chaotic trajectories will be emanated from the vortex by the incident current. Using the Chirikov criterion of resonance overlap, we estimate the radius of this regular vortex core and a range of the optimal frequencies, i.e. those frequencies of the incident current which provide a maximal possible stochastization of fluid particle trajectories. [ABSTRACT FROM AUTHOR]

Vortices generated at the open end of a planar shock tube are numerically simulated using the AUSM+ scheme. This scheme is known to have low numerical dissipation and therefore is suitable for capturing unsteady vortex motion. However, this low numerical dissipation can also cause oscillations in the vorticity field. Numerical experiments presented here highlight the effect of numerical dissipation on the simulated vortex, as well as the role played by turbulence models. Two turbulence models - the shear-stress-transport (SST) and its modified version for unsteady flows (SST-SAS) - are employed to observe the effect of including turbulence models in such complex flows where the vortex has an embedded shock. [ABSTRACT FROM AUTHOR]

An experimental investigation to predict the characteristics of scour vortices related to the scour depth of caisson piers was conducted. Two median size sediments were used as bed materials. Three types of piers, namely a cylindrical pier, a cylindrical pier with a caisson, and a nose pier were considered. The size and the rotational speed of the primary vortex were measured and correlated to the flow and pier parameters. The vortex power available to scour the sediment is related to the power provided by the vortex in the scour process. The equilibrium scour depth was predicted based on the concept of power available in the primary scour vortex equal to the resisting power of sediment in the scour hole. The prediction of the scour depth agrees well with literature data. [ABSTRACT FROM AUTHOR]

In this article we present a theoretical study for Fraunhofer diffraction of a Laguerre-Gaussian laser beam with zeroth radial mode number and azimuthal mode number l by a diffractive grating with embedded fork-shaped dislocations of integer order p. Analytical expressions describing the diffracted wave field amplitude and intensity distributions in the Fourier plane are deduced and analyzed. They are also followed by the vortex radii expressions. [ABSTRACT FROM AUTHOR]

The hydrodynamics and operational principle of the low-energy separator are described. This separator has two stages of separation: pre-separation and a twin separation unit composed of vortex-type separators. Multi-phase flow is fed to a pre-separation pipe designed to create stratified flow. Next, the stratified flow is split up into two streams, one formed mainly by gas and liquid, and another formed mainly by liquid and solid. These streams are diverted toward a twin vortex-type separator where each stream is separated into its individual phases. A three-layer model is used to study the pre-separation process, and a mechanistic-lagrangian model is used to analyze the flow into the twin-separation unit. The device is intended for use on facilities where the space is limited. Potential application of this separator includes, but is not restricted to, separation of multi-phase flows in surface equipment of under-balanced drilling, and in oil production facilities. [ABSTRACT FROM AUTHOR]

In this article we address two questions: Why do freely evolving vortices weaken on average, even when the viscosity is very small? Why, in the fluid's interior, away from vertical boundaries and under the influence of Earth's rotation and stable density stratification, do anticyclonic vortices become dominant over cyclonic ones when the Rossby number and deformation radius are finite? The context for answering these questions is a rotating, conservative, Shallow-water model with Asymmetric and Gradient-wind Balance approximations. The controlling mechanisms are vortex weakening under straining deformation (with a weakening that is substantially greater for strong cyclones than strong anticyclones) followed by a partially compensating vortex strengthening during a relaxation phase dominated by Vortex Rossby Waves (VRWs) and their eddy–mean interaction with the vortex. The outcome is a net, strain-induced vortex weakening that is greater for cyclones than anticyclones when the deformation radius is not large compared to the vortex radius and the Rossby number is not small. Furthermore, when the exterior strain flow is sustained, the vortex changes also are sustained: for small Rossby number (i.e., the quasigeostrophic limit, QG), vortices continue to weaken at a relatively modest rate, but for larger Rossby number, cyclones weaken strongly and anticyclones actually strengthen systematically when the deformation radius is comparable to the vortex radius. The sustained vortex changes are associated with strain-induced VRWs on the periphery of the mean vortex. It therefore seems likely that, in a complex flow with many vortices, anticyclonic dominance develops over a sequence of transient mutual straining events due to the greater robustness of anticyclones (and occasionally their net strengthening). [ABSTRACT FROM AUTHOR]